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Application of the boundary integral equation (BIE) method to transient response analysis of inclusions in a half space. (English) Zbl 0572.73029

Transient scattering of elastic waves by inclusions in a half space is investigated by the boundary integral equation (BIE) method. The formulation of BIE presented here is based on the Fourier transform method, and involves the analysis of transformed problems and the reconstitution of transient solutions by Fourier inversion. After the BIE has been solved numerically in the transformed domain, the transient wave fields are obtained with the help of the fast Fourier transform (FFT) algorithm. After confirmation of the accuracy of the present method, some numerical examples are shown for various inclusions in a half space, such as a cavity, an elastic inclusion, and a fluid inclusion.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74J20 Wave scattering in solid mechanics
74S99 Numerical and other methods in solid mechanics
74E05 Inhomogeneity in solid mechanics
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[1] Friedman, M. B.; Shaw, R., Diffraction of pulses by cylindrical obstacles of arbitrary cross section, J. Appl. Mech., 29, 40-46 (1962) · Zbl 0108.40204
[2] Shaw, R. P., Retarded potential approach to the scattering of elastic waves by rigid obstacles of arbitrary shape, J. Acoust. Soc. Amer., 44, 745-748 (1968) · Zbl 0167.53904
[3] Cole, D. M.; Kosloff, D. D.; Minister, J. B., A numerical boundary integral equation method for elastodynamics. I, Bull. Seism. Soc. Amer., 68, 1331-1357 (1978)
[4] Niwa, Y.; Fukui, T.; Kato, S.; Fujiki, K., An application of the integral equation method to two-dimensional elastodynamics, (Theoretical and Applied Mechanics, 28 (1980), Univ. Tokyo Press: Univ. Tokyo Press Tokyo), 281-290
[5] Fujiki, K., Analysis of the transient stresses around underground cavities by the integral equation method, (M.S. Thesis (1980), Kyoto University), (in Japanese)
[6] Mansur, W. J.; Brebbia, C. A., Transient elastodynamics using a time-stepping technique, (Boundary Elements (1983), Springer: Springer Berlin), 677-698 · Zbl 0546.73067
[7] Niwa, Y.; Kobayashi, S.; Yokoto, K., Application of integral equation method to the determination of static and steady-state dynamic stresses around many cavities of arbitrary shape, (Proc. Japan Soc. Civil Eng., 195 (1971)), 27-35, (in Japanese)
[8] Niwa, Y.; Kobayashi, S.; Azuma, N., An analysis of transient stresses produced around cavities of arbitrary shape during the passage of traveling waves, Mem. Fac. Eng. Kyoto Univ., 37, 28-46 (1975)
[9] Niwa, Y.; Kobayashi, S.; Fukui, T., Application of integral equation method to some geomechanical problems, (Proc. 2nd Internat. Conf. Numer. Meth. Geomech., Vol. 1 (1976)), 120-131
[10] Niwa, Y.; Kitahara, M.; Ikeda, H., The BIE approach to transient wave propagation problems around elastic inclusions, (Theoretical and Applied Mechanics, 32 (1984), Univ. Tokyo Press: Univ. Tokyo Press Tokyo), 183-198 · Zbl 0608.73038
[11] Kobayashi, S.; Nishimura, N., Transient stress analysis of tunnels and caverns of arbitrary shape due to travelling waves, (Developments in Boundary Element Methods, 2 (1982), Applied Science: Applied Science Barking), 177-210 · Zbl 0491.73095
[12] Niwa, Y.; Kitahara, M.; Hirose, S., Elastodynamic problems for inhomogeneous bodies, (Boundary Elements (1983), Springer: Springer Berlin), 751-763 · Zbl 0548.73062
[13] Niwa, Y.; Kitahara, M.; Hirose, S., Transient analysis of inhomogeneous structures by integral equation method, (Boundary Elements, VI (1984), Springer: Springer Berlin) · Zbl 0565.73072
[14] Kobayashi, S., Some problems of the boundary integral equation method in elastodynamics, (Boundary Elements (1983), Springer: Springer Berlin), 775-784 · Zbl 1236.93125
[15] Cruse, T. A.; Rizzo, F. J., A direct formulation and numerical solution of the general transient elastodynamic problem. I, J. Math. Anal. Appl., 22, 244-259 (1968) · Zbl 0167.16301
[16] Cruse, T. A., A direct formulation and numerical solution of the general transient elastodynamic problem. II, J. Math. Anal. Appl., 22, 341-355 (1968) · Zbl 0167.16302
[17] Manolis, G. D.; Beskos, D. E., Dynamic stress concentration studies by the integral equation method, (Proc. 2nd Internat. Symp. Innovative Numer. Anal. Eng. Sci. (1980)), 459-463 · Zbl 0459.73075
[18] Manolis, G. D.; Beskos, D. E., Dynamic stress concentration studies by boundary integrals and Laplace transform, Internat. J. Numer. Meth. Eng., 17, 573-599 (1981) · Zbl 0459.73075
[19] Manolis, G. D., A comparative study on three boundary element method approaches to problems in elastodynamics, Internat. J. Numer. Math. Eng., 19, 73-91 (1983) · Zbl 0497.73085
[20] Watson, J. O., Advanced implementation of the boundary element method for two- and three-dimensional elastostatics, (Developments in Boundary Element Methods, 1 (1979), Applied Science: Applied Science Barking), 31-63 · Zbl 0451.73075
[21] Kobayashi, S.; Nishimura, N., On the indeterminancy of BIE solutions for the exterior problems of time-harmonic elastodynamics and incompressible elastostatics, (Boundary Element Methods in Engineering (1982), Springer: Springer Berlin), 282-296 · Zbl 0499.73074
[22] Mow, C. C.; Mente, L. J., Dynamic stresses and displacements around cylindrical discontinuities due to plane harmonic shear waves, J. Appl. Mech., 30, 598-604 (1963)
[23] Pao, Y.-H., Dynamical stress concentration in an elastic plate, J. Appl. Mech., 29, 299-305 (1962) · Zbl 0111.22102
[24] Garnet, H.; Crouzet-Pascal, J., Transient response of a circular cylinder of arbitrary thickness, in an elastic medium, to a plane dilatational wave, J. Appl. Mech., 33, 521-531 (1966)
[25] Ewing, W. M.; Jardetzky, W. S.; Press, F., Elastic Waves in Layered Media (1957), McGraw-Hill: McGraw-Hill New York · Zbl 0083.23705
[26] Achenbach, J. D., Wave Propagation in Elastic Solids (1973), North-Holland: North-Holland Amsterdam · Zbl 0268.73005
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